Answers
1) F(x) is narrower than G(x)
This implies G(x) is multiplied by a number greater than 1
2) F(x) is above G(x) by 1 unit
This implies vertical shift of , so a 1 is added to G(x).
Among the given options, only option B fulfills these two criteria.
So the answer is option B
Related Questions
What is the simplified form of 1 over x minus 2 over x squared plus x ?
Answers
Step-by-step explanation:
Given expression [tex]\frac{1}{x} -\frac{2}{x^2+x}[/tex].
Let is factor second denominator [tex]x^2+x[/tex] first.
Factoring out GCF x we get
[tex]x^2+x= x(x+1)[/tex]
Rewriting the equation
[tex]\frac{1}{x} -\frac{2}{x^2+x} = \frac{1}{x} - \frac{2}{x(x+1)}[/tex]
Now, we need to find the lowest common denominator of x and x(x+1).
The lowest common denominator of x and x(x+1) is x(x+1).
So, we need to multiply first fraction by (x+1) in top and bottom to get lowest common denominator x(x+1) under first fraction.
[tex]\frac{1}{x} - \frac{2}{x(x+1)} = \frac{1(x+1)}{x(x+1)} - \frac{2}{x(x+1)}[/tex]
[tex]= \frac{x+1}{x(x+1)} - \frac{2}{x(x+1)}[/tex]
We got denominators same.
Therefore, subtracting numerators, we get
[tex]=\frac{x+1-2}{x(x+1)}[/tex]
[tex]\frac{x-1}{x(x+1)}[/tex].
Therefore, simplified form is [tex]\frac{x-1}{x(x+1)}[/tex].
Simplify (x − 4)(x2 − 2x − 3).
Answers
Start with x, that would be
x²·x - 2x·x - 3x
x³ - 2x² - 3x
Now distribute -4.
-4x² + 8x + 12
Now put them together:
x³ - 2x² - 3x + (-4x² + 8x + 12)
Combine like terms:
x³ - 6x² + 5x + 12
Final answer: x³ - 6x² + 5x + 12
Hope this helps.
when Derek planted a tree it was 36 inches tall the tree grew one and one fourth inches per year the tree is now forty four and three fourths how many years ago did Derek plant the tree
Answers
Answer:
7
Step-by-step explanation:
Figure out all the fractions in decimal form
44 3/4= 44.75
1 1/4= 1.25
Subtract:
44.75- 36= 8.75
Divide:
8.75/1.25= 7
The answer therefore is 7!
Hope this helps!!!
Which of these is a point-slope equation of the line that is perpendicular to y-25=2(x-10) and passes through (-3,7)
Answers
We know the slope to be 2 because lines that are parallel have the same slope. Then we can solve using slope-intercept form and the known point.
y = mx + b ----> Input known values
7 = (2)(-3) + b ---> Multiple
7 = -6 + b ----> Subtract 3 from both sides
13 = b
Now we can use the y-intercept found and the slope to write the equation above.
Answer: y - 7= -1/2 (x+3)
Step-by-step explanation:
Sometimes one form is more beneficial than the other. Identify which form would be more helpful if you needed to do each task listed below and explain why. a. Factor the equation. b. Graph the parabola. c. Identify the vertex, minimum, or maximum of the parabola. d. Solve the equation using the quadratic formula.
Answers
The easiest one to use if it is available to you, is factoring. The quadratic may not be factorable. But if it is and you can see it, then this gives you 2 points immediately (the roots) and a third without much trouble (the y intercept). Factoring will also give you the x value of the vertex. (Find the average between the 2 roots)
This needs an example
Suppose you have y = (x - 5)(x - 9) The roots are 5 and 9, correct? So the x value of the vertex is (5 + 9)/2 = 7 It always works.
Completing the square always gives you the minimum or maximum right away. For example if you have y = (x - 2)^2 - 5 it means you have the vertex at (2,-5) You can get the roots easily enough. So this form is useful, but not as sure as the quadratic equation or as simple as factoring.
Graphing is the most certain way to check your answer. I find it the most useful thing to do with modern computers. There are all sorts of things that a graph will reveal that algebra by itself might be laborious and prone to leading you to mistakes. Graphing tends to correct that problem.
If a circle has a circumference of 10 pi inches, then what is the area of the same circle in square inches?
Answers
To find the area of the circle, use the formula A = πr² and solve for the radius with the equation C = 2πr. Then, substitute the radius value into the area formula to find the area.
Explanation:In order to find the area of the circle, we need to use the formula A = πr², where A is the area and r is the radius of the circle. In this case, we are given that the circumference of the circle is 10π inches.
We know that the formula for circumference of a circle is C = 2πr, where C is the circumference and r is the radius. We can set up an equation to solve for the radius:
10π = 2πrr = 10/2r = 5 inchesNow that we know the radius is 5 inches, we can use the formula A = πr² to find the area:
A = π(5)²A = 25π square inchesSo, the area of the circle is 25π square inches.
The area of the circle is [tex]\( 25\pi \)[/tex] square inches.
To find the area of the circle, we first need to determine the radius of the circle. The circumference [tex]C[/tex] of a circle is given by the formula [tex]\( C = 2\pi r \),[/tex] where [tex]r[/tex] is the radius. Given that the circumference is [tex]\( 10\pi \)[/tex] inches, we can solve for the radius:
[tex]\[ 10\pi = 2\pi r \][/tex]
[tex]\[ r = \frac{10\pi}{2\pi} \][/tex]
[tex]\[ r = 5 \][/tex]
Now that we have the radius, we can find the area [tex]\( A \)[/tex] of the circle using the formula [tex]\( A = \pi r^2 \):[/tex]
[tex]\[ A = \pi (5)^2 \][/tex]
[tex]\[ A = 25\pi \][/tex]
Therefore, the area of the circle is [tex]\( 25\pi \)[/tex] square inches.
The equation sin(40o) = can be used to determine the length of line segment AC. What is the length of ? Round to the nearest tenth._____cm
Answers
Answer:
12.9 centimetersStep-by-step explanation:
The given equation is
[tex]sin(40\°)=\frac{b}{20}[/tex]
Where [tex]b[/tex] represents the length of the segment AC, according to the given graph.
To find [tex]b[/tex] we just need to isolate it in the given equation,
[tex]b=20sin(40\°)[/tex]
Then, we know that [tex]sin(40\°) \approx 0.64[/tex], so
[tex]b=20(0.64)=12.9cm[/tex]
Therefore, the length of segment AC is 12.9 centimeters, rounded to the nearest tenth.
Answer:
B
Step-by-step explanation:
edge 2021
Graph the quadratic function
F(x)=3x^2+6x-24
Answers
F (x) = 3x ^ 2 + 6x-24
We observe that it is a quadratic equation.
The graph is therefore a parabola.
Its cut points are:
(-4, 0)
(2, 0)
Answer:
See attached image to see graph of the function
An oil company is considering 2 sites on which to drill, described as follows:
Site A: profit of oil is found: $60 million
Loss if no oil is found: $5 million
Probability of finding oil: 0.2
Site B: profit of oil is found: $90 million
Loss of no oil is found: 0.1
A: Which site has the larger expected profit?
B: if the expected profit for both sites is not the same, by how much is the expected profit larger?
Answers
B) the difference between amount of profitmade is 30 million.
a disk jockey wants to select five songs from a new CD that contains 12 songs. How many ways can a disc jockey choose 5 songs
Answers
The formula for combinations is: n!/r!(n-r)! where n is the total number possible options and r is the number taken at a time. For this problem n = 12 and r = 5
12!/5!7! = 792 different possible combinations.
The formula for a permutation is n!/(n-r)! where n and r represent the same things as above.
12!/7! = 95,040 different possible permutations
The reason for more permutation than combinations is because if you have 12 songs think of them as 1,2,3,4,5,6,7,8,9,10,11,12. Under a combination songs 1,3,6,9 and 3,6,1,9 are the same, but in a permutation the order matters so these are both different possible outcomes.
Answer: There are 792 ways to pick 5 songs from 12 songs.
Gabriel determined that his total cost would be represented by 2.5x + 2y – 2. His sister states that the expression should be x + x + 0.5x + y + y – 2. Who is correct? Explain.
Answers
Gabriel's representation is a more compact form of his sister's representation, but they mean the same thing.*
_____
* In some computer applications, one gets a different result from computing 2.5x than from computing x + x + 0.5x. This has to do with the way numbers are represented in the computer and the way they are rounded during multiplication and/or addition. For the purposes of algebra, the expressions mean the same thing.
Gabriel and his sister's expression mean the same; However, the information available is not sufficient to determine if they are correct or not.
According to the question;
Gabriel representation is; 2.5x + 2y – 2.His sister's expression is; x + x + 0.5x + y + y – 2.Upon computation; we find out that the expressions supplied by Gabriel and his sister are the same.
However, we must note that the information available is not sufficient to determine if both parties are correct or not.
Ultimately, if Gabriel is correct, then his sister is too and if otherwise, she is not correct too.
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The seventh-grade class is building target areas for a PE activity. The bases for the game will be in a circular shape. The diameter of each circle is 3 feet. Approximately, how many square feet of the turf needs to be painted for a base circle? Use 3.14 for π and round your answer to the nearest tenth. 7.1 square feet 9.4 square feet 18.8 square feet 28.3 square feet
Answers
A = pi * (1.5)²
A = pi * 2.25
A = 3.14 * 2.25
A = 7.065 ≈ 7.1
7.1 feet² is your answer.
Let area = A
Let π= 3.14
Let radius = 1.5
The formula is as followed, you fill in the blanks:
[tex]A= \pi r^2 \\ (Area = 3.14 * radius^2 [/tex]
The answer exact answer is 7.07, but if you were to round it, because you want an approximate answer it would be 7.1 square feet.
Your answer from your choices given is bolded, and the work is in the picture:
- 7.1 square feet
- 9.4 square feet
- 18.8 square feet
- 28.3 square feet
Author's Note:
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All I need is the following:
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For what values of m does the graph of y = mx2 – 5x – 2 have no x-intercepts?
Answers
Answer: The graph of y=mx^2-5x-2 have no x-intercepts for m<-25/8
Solution:
y=mx^2-5x-2
To find x-intercepts we must equal y to zero:
y=0→mx^2-5x-2=0
This is a quadratic equation, and we can solve it using the quadratic formula:
ax^2+bx+c=0; a=m, b=-5, c=-2
x=[-b +- sqrt( b^2-4ac) ] / (2a)
x=[-(-5) +- sqrt( (-5)^2-4(m)(-2) ) ] / (2(m))
x=[5 +- sqrt(25+8m)] / (2m)
This equation doesn't have solution (no x-intercepts) if:
25+8m<0
This is an inequality. Solving for m: Subtracting 25 both sides of the inequality:
25+8m-25<0-25
8m<-25
Dividing both sides of the inequality by 8:
(8m) / 8 < (-25) / 8
m<-25/8
Answer: The graph of y=mx^2-5x-2 heve no x-intercepts for m<-25/8
SOMEONE PLEASE HELP ASAP
Answers
0.2; 0.2*(-0.3); 0.2*(-0.3)*(-0.3); 0.2*(-0.3)*(-0.3)*(-0.3);... etc.
if the first term of this sequence is n=1, then only 'C' is the right answer:
[tex]a_n=0.2*(-0.3)^{n-1}.[/tex]
[tex] a_{n}= a_{1}(r)^{n-1} [/tex]
Here, [tex]a_{1}= [/tex]First Term = 0.2
r = Common Ratio = - 0.06/0.2 = -0.3
Using these value in above formula, we can write the explicit formula of the sequence as:[tex]a_{n}=0.2(-0.3)^{n-1} [/tex]
So, option C gives the correct answer
A jogger goes 1.2 mi west then turns south. If the jogger finishes 1.3 mi from the starting point, how far south did the jogger go?
Answers
0.5 miles
The jogger's movement can be represented as a right-angled triangle, where the legs of the triangle represent the distances traveled west and south, and the hypotenuse is the direct distance from the starting point to the finishing point. To solve for the distance the jogger traveled south, we need to use the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is expressed as c2 = a2 + b2.
Using the Pythagorean theorem:
1.32 = 1.22 + b2
Therefore:
b2 = 1.32 - 1.22
b2 = 1.69 - 1.44
b2 = 0.25
b = [tex]\sqrt{0.25}[/tex]
b = 0.5 mi
So, the jogger traveled 0.5 miles south.
HELP!!! First gets Top Answer!!!
See image for more details
- Use your calculator and hit the "2nd" button and then the log button which should be the 10x function. Your answer should be 0.00355.
Answers
H=10^(-pH)
log H = -pH
pH=-logH => so it is affirmed that it is -.40
The concentration of hydrogen ions ([H+]) in the solution with a pH of 2.45 is approximately 0.00355 moles per liter (M).
The process you described is correct for finding the concentration of hydrogen ions ([H+]) from a given pH value using the formula [H+] = 10^(-pH).
Here's how you would calculate the [H+] concentration for a solution with a pH of 2.45:
a) Take the negative of the pH value:
-log(2.45) = -0.389
b) Now, use your calculator and calculate 10 raised to the power of the negative pH value:
10^(-0.389) ≈ 0.00355
So, the concentration of hydrogen ions ([H+]) in the solution with a pH of 2.45 is approximately 0.00355 moles per liter (M).
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Using the graph below, what are the common ratio and the general term equation, an, of the geometric sequence?
Hint: an = a1(r)n − 1, where a1 is the first term and r is the common ratio.
Answers
an=a1(r)^(n-1)
where:
a1= first term
r=common ratio
n=number of terms:
from the graph, our sequence is:
-32,-24,-18,...
where:
a1=-32
a2=-24
a3=-18
thus
common ratio, r=-24/-32=3/4
thus the general form will be:
an=-32(3/4)^(n-1)
Please help with the question,
Answers
The explanation is shown below:
1. To solve the problem shown in the figure above, you must apply the following proccedure:
2. You have that the roots of the quadratic equation shown in the figure attached in the problem are:
x=-1±i
3. Then, you know the quadratic formula to solve quadratic equations, which is:
(-b±√(b^2-4ac))/2a
4. You can see in the figure that a=1 and c=2; then, by analizing this, you can conclude that the coefficient b is:
b=-2
5. Therefore, you can conclude tha the quadratic equation is:
x^2-2x+2=0
6. If you want to verify it, apply the quadratic formula to the quadratic equation shown above and you will obtain the roots shown in the figure.
To form a quadratic equation, let α and β be the two roots.
Let us assume that the required equation be ax22 + bx + c = 0 (a ≠ 0).
According to the problem, roots of this equation are α and β.
Therefore,
α + β = - baba and αβ = caca.
Now, ax22 + bx + c = 0
⇒ x22 + babax + caca = 0 (Since, a ≠ 0)
⇒ x22 - (α + β)x + αβ = 0, [Since, α + β = -baba and αβ = caca]
⇒ x22 - (sum of the roots)x + product of the roots = 0
⇒ x22 - Sx + P = 0, where S = sum of the roots and P = product of the roots ............... (i)
Formula (i) is used for the formation of a quadratic equation when its roots are given.
Given the roots: (-1+-i)
where; i=sqrt(-1)
Thus, the answer is (2x)
You can also do checking to verify if x^2+2x+2 will have roots equal to (-1+-i)
Which of the following are examples of exponential decay?
Answers
the rate is going to be less than 1, and it is going to continue,
it should look for example like
x*1/2*1/2*....
The answers should be B,C,D.
Answer: B,C,D
Step-by-step explanation:
What is the mode of the following numbers? 8,10,10,10,6,7,8
Answers
The mode is the number that appears most frequently in a data set.
In the data set shown here, 10 appears more time than any other number which means that 10 is the mode.
Therefore, the mode of the data set shown here is 10.
for every 5 serves Gabby makes tanning makes 3 at volleyball practice Tammy makes 21 serves how many serves did Gabby make show your answer will mark brainiest
Answers
divide 21 by 3 ( 21/3 = 7)
no multiply 7 by 5 ( 7 x 5 = 35)
Gabby made 35 serves
Steve puts only dimes and quarters into his piggy bank. Right now he has five more dimes than quarters there, and they make exactly $74! How many quarters and how many dimes are there in Steve’s piggy bank?
Answers
$74=7400 cents
Then
(25x+10(x+5))=(25x+10x+50)=(35x+50) cents.
35x+50=7400
35x=7400-50
35x=7350
x=7350/35
x=210 quarters
x+5=210+5=215 dimes
210 quarters and 215 dimes
Answer:
215 dimes and 210 quarters
Step-by-step explanation:
Quarters are x
dimes are x+5
.25x+.10(x+5)=74
.25x+.10x+.5=74
.35x=73.5
x=210 quarters or $52.50
x+5=215 dimes or $21.50
Add to $74.
Maya spent her allowance on playing an arcade game a few times and riding the Ferris wheel more than once.
Write about what additional information you would need to create a two-variable equation for the scenario. What kind of problem could you solve with your equation?
Answers
Hope this Helps!!
Answer:
To write a two-variable equation, I would first need to know how much Maya’s allowance was. Then, I would need the cost of playing the arcade game and of riding the Ferris wheel. I could let the equation be cost of playing the arcade games plus cost of riding the Ferris wheel equals the total allowance. My variables would represent the number of times Maya played the arcade game and the number of times she rode the Ferris wheel. With this equation I could solve for how many times she rode the Ferris wheel given the number of times she played the arcade game.
Step-by-step explanation:
You earn $20.00 per hour at your job. If you get a 10% raise at the end of each year, what will your hourly rate, h, be after 8 years? Use the equation h=C(l+r)^t, where C is the beginning hourly rate, r is the growth rate, and t is time in years. A. $36.00 B. $22.00 C. $47.27 D. $42.87
Answers
Find the value of x.
Pls help
Answers
Something important to remember, vertical angles that share the same vertex have the same measure, and are congruent.
So, if that one angle is 58, x would also equal 58.
58 is the answer.
I hope this helps!
~kaikers
Consider the graphs f(x) = log10x and g(x) = a · log10x.
What happens to the graph of g(x) = a · log10x if a is –7? Check all that apply.
a.The graph is stretched vertically.
b.The graph will shift a units to the right.
c.The graph is compressed.
d.The graph is reflected across the x-axis.
e.The graph will shift a units to the left.
Answers
Therefore, the correct answers are a and d.
Decide whether to reject h 0 for the level of significance ΅ . right - tailed test z = 1.43 ΅ = 0.05 22) the p - value for a hypothesis test is p = 0.006. do you reject or fail to reject h 0 when the level of significance is ΅ = 0.01? 23) find the p - value for the hypothesis test with the standardized test statistic z. decide whether to reject
Answers
To decide whether to reject H0 for the level of significance ΅ in a right-tailed test, we compare the p-value to the level of significance. In this case, the p-value for the hypothesis test is 0.006 and the level of significance is 0.01. Since the p-value (0.006) is less than the level of significance (0.01), we reject H0.
Explanation:To decide whether to reject H0 for the level of significance ΅ in a right-tailed test, we compare the p-value to the level of significance. In this case, the p-value for the hypothesis test is 0.006 and the level of significance is 0.01. Since the p-value (0.006) is less than the level of significance (0.01), we reject H0.
For the second question, the p-value is not provided, so we cannot make a decision based on the information given.
The price of a dozen roses in the united states is $30. if $0.3472 can purchase 1.00 turkish lira, how much does the same dozen roses cost in turkey if purchasing power parity holds
Answers
0.3472 $ -----> 1.00 turkish lira
$ 30 -----------> x
Clearing x we have:
x = (30 / 0.3472) * (1)
x = 86.40552995 turkish lira
Answer:
the same dozen roses costs:
x = 86.40552995 turkish lira
well $30 is 185.02 in turkish lira.
hello can you please help me posted picture of question
Answers
Number of players to be selected = 2
We can find the number of ways of selecting the player using permutations.
Ways to select 2 players from 9 = 9P2
[tex]= \frac{9!}{7!} \\ \\ =9*8 \\ \\ =72 [/tex]
Thus, the answer is option C
When a number is decreased by 24% of itself the result is 171. What is the number?
Answers
x----------> original number
we know that
if a number is decreased by 24% of itself the result is
x*(100%-24%)/100%------> x*0.76
171=0.76*x
x=171/0.76---------> 225
the answer is
the number is 225